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**Unformatted text preview: **Generally speaking, a differential equation is an equation that contains a derivative. Determine all solutions of the differential equation y = 1 2 y . The equation has the form y = ky with k = 1/2. Therefore, any solution of the equation has the form y = 1 2 y y = Ce 1 2 x where C is a constant. Determine all functions y = f ( x ) such that y = 3 y and f (0) = . The equation has the form y = ky with k = 3. Therefore, for some constant C . We also require that f (0) = . That is, So C = and...

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